Multicarrier systems, such as orthogonal frequency-division multiplexing (OFDM), are widely employed in broadband communication due to their high spectrum efficiency and simple frequency domain equalisation in dense multipath channels. Spectrum shaping, in particular sidelobe suppression, is an important design consideration in such systems. The waveform of each OFDM subcarrier is inherently a sine function, and the power of sine sidelobes decays slowly as f2, where f is the frequency distance to the main lobe. The problem of sidelobe suppression becomes more significant when multicarrier modulation is applied in cognitive radio, where instantaneously spare frequency bands in primary systems are proposed to be used by intelligent secondary systems. Such secondary systems need to ensure that their transmitted signal has very sharp spectrum roll-off to maximise their usable bandwidth and minimise interference to primary systems.
Conventionally, time-domain windowing, such as raised cosine windowing, is applied for sidelobe suppression (out-of-band emission reduction). FIG. 1 illustrates an OFDM transmitter 100 with conventional sidelobe suppression. The transmitter 100 has an Inverse Fast Fourier Transform module 110 to convert a sequence of input symbols to a time-domain OFDM symbol. The first guarding prefix is then added to the OFDM symbol at the module 120 to avoid the interference due to multipath delay spread, and the second guarding prefix is added at the module 130 to avoid distortions caused by the time-domain windowing for sidelobe suppression performed by the module 140. A digital-to-analog conversion module 150 converts the windowed time-domain OFDM symbol to an analog waveform.
The length of the guarding interval of the second guarding prefix added at the module 130 depends on the spectrum sharpness to be achieved. The sharper the roll-off of the spectrum needs to be, the longer the guarding interval required. Furthermore, some guarding subcarriers in the two edges of the band are also needed in order to complement the windowing effect. As a result, the spectrum efficiency can be significantly reduced by the windowing module 140. In addition, it is difficult for the time-domain windowing module 140 to achieve large enough out-of-band emission reduction in cognitive radios where multicarrier modulation over non-contiguous subbands is frequently employed. In these applications, a straightforward technique is to apply notch filters to the unallocated subbands. However, a digital implementation of a notch filter would increase the processing complexity considerably, and an analog implementation would be costly and difficult to adapt to dynamic band allocation.
Recently, some signal pre-distortion (precoding) techniques have been proposed for sidelobe suppression. These techniques can be classified into two classes: 1) cancelling out-of-band emission from data subcarriers by optimising the signals at reserved subcarriers; and 2) pre-distorting data symbols to minimise their combined out-of-band emission. Class 1 techniques can achieve good sidelobe suppression, but lead to signal-to-noise power ratio (SNR) degradation in the receiver as power is wasted at the reserved subcarriers. Furthermore, their complexity, which is proportional to the number of points to be cancelled in the sidelobe, could be quite high for large suppression. Class 2 techniques optimise a precoding matrix via some cost function of the out-of-band emission. These techniques have the advantage of maintaining the receiver SNR by using an orthogonal precoding matrix. However, their computational complexity is proportional to the square of the number of subcarriers in the band of interest and is therefore impractical for most applications.